Example 39

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EXAMPLE 39 Calculating numbers of permutations

Find the following numbers of permutations:

$_{5} P_{2}$
$_{6} P_{2}$
$_{6} P_{6}$

Solution

$_{5} P_{2} = \frac{5!}{(5 - 2)!} = \frac{5 \cdot 4 \cdot 3!}{3!} = 20$
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$_{6} P_{2} = \frac{6!}{(6 - 2)!} = \frac{6 \cdot 5 \cdot 4!}{4!} = 30$
$_{6} P_{6} = \frac{6!}{(6 - 6)!} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1!}{0!} = 720$

NOW YOU CAN DO

Exercises 25–32.